I've created bare git repositories on Dropbox before and haven't had any problems using them as git remotes. They've only been used by me though, so things might get more tricky if you need multi-user access.
A few have mentioned syncing issues, so if you try the Dropbox approach, think about what the worst that could happen might be? If you can live with that, then give it a go. You can always setup other git remotes for GitHub and / or Bitbucket as well, in addition to a Dropbox remote, if you worried about syncing issues (although you'd obviously have to manually push / pull to these).
A few have mentioned syncing issues, so if you try the Dropbox approach, think about what the worst that could happen might be? If you can live with that, then give it a go. You can always setup other git remotes for GitHub and / or Bitbucket as well, in addition to a Dropbox remote, if you worried about syncing issues (although you'd obviously have to manually push / pull to these).